Motivated by recent breakthrough in molecular beam epitaxy of GaAs/AlGaAs quantum wells [Y. J. Chung \textit{ et al.}, Nature Materials \textbf{ 20}, 632 (2021)], we examine contributions to mobility and quantum mobility from various scattering mechanisms and their dependencies on the electron density. We find that at lower electron densities, $n_e \lesssim 1 \times 10^{ 11}$ cm$^{ -2}$, both transport and quantum mobility are limited by unintentional background impurities and follow a power law dependence, $\propto n_e^{ \alpha}$, with $\alpha \approx 0.85$. Our predictions for quantum mobility are in reasonable agreement with an estimate obtained from the resistivity at filling factor $\nu= 1/2$ in a sample of Y. J. Chung \textit{ et al.} with $n_e = 1 \times 10^{ 11}$ cm$^{ -2}$. Consideration of other scattering mechanisms indicates that interface roughness (remote donors) is a likely limiting factor of transport (quantum) mobility at higher electron densities. Future measurements of quantum mobility should yield information on the distribution of background impurities in GaAs and AlGaAs.
Categories: cond-mat.mes-hall cond-mat.mtrl-sci